However, as noticed by Damour and Blanchet in. [1]}, the evaluation of the conservative dynamics, by focusing only on the near zone contribution, breaks down at 4PN order due to the appearance of infrared divergences. Indeed, at this level of accuracy, is crucial to take into account that the gravitational propagator in the curved space-time, generated by the binary system, contains a significant tail contribution whose support is not limited to light-like intervals, but extends to strongly time non-local intervals.
